%0 Journal Article
%T Pair Difference Cordiality of Some Snake and Butterfly Graphs
%J Journal of Algorithms and Computation
%I University of Tehran
%Z 2476-2776
%A Ponraj, R
%A Gayathri, A
%A Somasundaram, S
%D 2021
%\ 06/01/2021
%V 53
%N 1
%P 149-163
%! Pair Difference Cordiality of Some Snake and Butterfly Graphs
%K Triangular snake
%K Alternate triangular snake
%K Quadrilatral Snake
%K Alternate Quadrilatral Snake
%K Butter fly
%R 10.22059/jac.2021.81649
%X noindent Let $G = (V, E)$ be a $(p,q)$ graph.\Define begin{equation*}rho =begin{cases}frac{p}{2} ,& text{if $p$ is even}\frac{p-1}{2} ,& text{if $p$ is odd}\end{cases}end{equation*}\ and $L = {pm1 ,pm2, pm3 , cdots ,pmrho}$ called the set of labels.\noindent Consider a mapping $f : V longrightarrow L$ by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when $p$ is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge $uv$ of $G$ there exists a labeling $left|f(u) - f(v)right|$ such that $left|Delta_{f_1} - Delta_{f_1^c}right| leq 1$, where $Delta_{f_1}$ and $Delta_{f_1^c}$ respectively denote the number of edges labeled with $1$ and number of edges not labeled with $1$. A graph $G$ for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate the pair difference cordial labeling behavior of some snake and butterfly graphs.
%U https://jac.ut.ac.ir/article_81649_9670058e7708586f959c57de1e3434f5.pdf